Cloth simulation pulling skirt upward
For cloth collision (and, indeed, any collision in Blender) it is important to ensure that the simulation starts without the meshes overlapping - otherwise they will instantly repel and can cause unpredicted results.

With cloth, if the ‘garments’ are intended to be quite tightly fitting you can use sewing springs or cloth shrinking to bring the garment together around the model once the simulation starts. Those options are found within the Cloth Sewing Springs panel.